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1. Suppose that ak 20 for all k E N. (a) Use the arithmetic-geometric mean inequality to show that if the series a k=1 converges, then converges. k=1 k (b) If a converges, does it imply that k=1 i. 1 ak converges? k=1 ii. Ea converges?

1. Suppose that ak 20 for all k E N. (a) Use the arithmetic-geometric mean inequality to show that if the series a k=1 converges, then converges. k=1 k (b) If a converges, does it imply that k=1 i. 1 ak converges? k=1 ii. Ea converges?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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1. Suppose that ak ≥ 0 for all k € N. (a) Use the arithmetic-geometric mean inequality to show that if the series Σ₁a² k=1 ak converges, then Σ k=1 k converges. (b) If a converges, does it imply that k=1 i. Σ1 ak converges? k=1 3 ii. Ea converges? k=1
Transcribed Image Text:1. Suppose that ak ≥ 0 for all k € N. (a) Use the arithmetic-geometric mean inequality to show that if the series Σ₁a² k=1 ak converges, then Σ k=1 k converges. (b) If a converges, does it imply that k=1 i. Σ1 ak converges? k=1 3 ii. Ea converges? k=1
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